Applications of Molecular Orbit Theory

Electronic configuration and Molecular Behavior:

• The distribution of electrons among various molecular orbitals is called the electronic configuration of the molecule.

Important information of configuration:

a) Stability of Molecules:

1. The molecule is stable if N_B is greater than N_A
2. The molecule is unstable if N_B is less than N_A.
   Where
   N_B → Bonding e⁻s
   N_A → Anti – Bonding e⁻s

b) Bond order:

Bond order is defined as one half the difference between the number of electrons present in the bonding and the anti-bonding orbitals.

Bond order = ½ [N_B – N_A]

The rules discussed in the above regarding the stability of the molecule can be restated in terms of Bond order as follows.

1. A positive Bond order means a stable molecule while negative (or) zero bond order means an unstable molecule.
2. Nature of Bond: Integral bond order values of 1, 2 (or) 3 correspond to single, double (or) triple bonds respectively.

c) Bond Length:

• The bond order between two atoms in a molecule may be taken as an approximate measure of the Bond length.
• Bond length decreases bond order increases.

d) Magnetic Nature:

• If all the molecular orbitals in a molecule are doubly occupied the substance is diagrammatic.
• If one (or) more molecular orbitals are singly occupied it is paramagnetic.
  EX: O₂ Molecule

Bonding in some Homonuclear diatomic molecules:

1. Hydrogen Molecule (H₂):

• There are 2 electrons in hydrogen molecule which are present in σ1S molecular orbital so electronic configuration of hydrogen molecule is H₂ : (σ1S)²
  The bond order of H₂ molecule can be calculated as given below

            Bond order \(=\frac{{{N}_{B}}-{{N}_{a}}}{2}=\frac{2-2}{2}=1\)

• Since there is no unpaired electron in hydrogen molecule, therefore it is diamagnetic.

2. Helium molecule (He₂):

• In He₂ molecule there are 4 electrons. These electrons will be accommodated in σ1S and σ*1S molecular orbital leading to electronic configuration.
  He₂ : (σ1S)² (σ*1S)²
• Bond order He₂ is ½ (2 – 2) = 0
• He₂ Molecule is therefore unstable and does not exist.

3. Lithium Molecule (Li₂):

• The electronic configuration of lithium is 1S², 2S¹. There are six electrons in Li₂ the electron configuration of Li₂ molecule therefore is Li₂ : (σ1S)² (σ*1S)² (σ2S)²
• The above configuration is also written as KK (σ2S)² where KK represents the closed K shell structure (σ1S)² (σ*1S)²
• There are four electrons present in bonding molecular orbitals and two electrons in anti-bonding molecular orbitals.
  Bond order ½ [4 – 1] = 1
• It has no unpaired electrons so it is diamagnetic.

 4. Oxygen molecule (O₂):

• The electronic configuration of oxygen atom is 1S²2S²2P⁴ each oxygen atom has 8 electrons hence, in O₂ molecule there are 16 electrons. The electronic configuration of O₂ molecule therefore O₂ : (σ1S)² (σ*1S)² (σ2S)² (σ*2S)² (σ2P_Z)² (π2P²_X ≡ π2P²_Y) (π*2P¹_X ≡ π*2P¹_Y)
• From the electronic configuration of O₂ molecule, t is clear that ten electrons are present in anti-bonding molecular orbitals and six electrons are present in anti-bonding molecular orbitals.
  Its bond order = ½ [N_B – N_A] = ½ [10 – 6] = 4.
• It may be noted that it contains two unpaired electrons π*2P_X and π*2P_Y molecular orbitals.
• O₂ Molecule should be paramagnetic.

5. Nitrogen molecule (N₂):

• The electronic configuration of Nitrogen is 1s² 2S² 2P³, there are 14 electrons in N₂. The electronic configuration of N₂ : σ1S² < σ*1S² < σ2S² < σ*2S² < (π2P²_x = π2P²_y) < σ2P²_z)
• Bond order of N₂ = ½ [10 – 4] = 3
• There is no unpaired electron in the electronic configuration of N₂.
  It is diamagnetic in nature.